While I'm sure that Spartacus would have learned Latin later in his life, it most likely was not his first language. He was mentioned in Plutarch's works as a "Thracian of nomadic stock." I would posit that he would have grown up speaking the Thracian language which is an Indo-European language, so it's related to Greek and Latin (as well as the Germanic languages and all the others in the Indo-European language family, but that would be a huge tangent here) although it was quite a bit different. By Spartacus' slave, gladiator and slave revolt days, he would have likely been primarily speaking the vulgar Latin of the era.

Edit: accidentally a word.